Back to Departmental Colloquium: Fall 2022
Departmental Colloquium
Date: Thursday, Oct 6, 2022
Time: 4:00PM - 5:00PM
Location: JWB 335
Peter Bates
Michigan State University
Title |
How should a drop of liquid move on a smooth curved surface in zero gravity? |
Abstract |
Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970’s to infinite-dimensional semi-dynamical systems. This represents joint work with Kening Lu and Chongchun Zeng. |
Applied Mathematics
Dynamical Systems
Paul Fife Memorial Lecture Series